Question

Listed below are the numbers of hurricanes that occurred in each year in a certain region. The data are listed in order by year. Find the​ range, variance, and standard deviation for the given sample data. Include appropriate units in the results. What important feature of the data is not revealed by any of the measures of​ variation? 11, 6, 10, 10, 8, 10, 17, 8, 1, 10, 7, 5, 19, 15

The range of the sample data is ___ (plus one of the following)

hurricanes squared .hurricanes2.

years squared .years2.

years.years.

hurricanes.hurricanes.

​(Round to one decimal place as​ needed.)

The standard deviation of the sample data is ____ (plus one of the following)

a. hurricanes.hurricanes.

b. years squared .years2.

c. hurricanes squared .hurricanes2.

d. years.years.

​(Round to one decimal place as​ needed.)

The variance of the sample data is______? (plus one of the following)

a. years.years.

b. hurricanes squared .hurricanes2.

c. hurricanes.hurricanes.

d.years squared .years2.

​(Round to one decimal place as​ needed.)

What important feature of the data is not revealed through the different measures of​ variation?

A. The measures of variation do not reveal the difference between the largest number of hurricanes and the smallest number of hurricanes in the data.

B. The measures of variation reveal no information about the scale of the data.

C. The measures of variation reveal nothing about the pattern over time.

D.The measures of variation reveal nothing about how the numbers of hurricanes are spread.

Answer 1

Solution :

Listed below are the numbers of hurricanes that occurred in each year in a certain region. The data are listed in order by year. We have to find the​ range, variance, and standard deviation for the given sample data including the appropriate units in the results. We also have to find the out the important feature of the data that is not revealed by any of the measures of​ variation ... !! We have the following data with us :

Data provided

Numbers of hurricanes that occurred in each year in a certain region
11	6	10	10	8	10	17	8	1	10	7	5	19	15

Let "X" be the Numbers of hurricanes that occurred in each year in a certain region.

Let "n" be the total Sample size of the data.

(i) The Range of the sample data is given as,

The Mean of the sample data is given as,

(ii) The Standard Deviation of the sample data is given as,

(iii) The Variance of the sample data is given as,

The below table shows all the relevant calculations for obtaining the above statistics ::

Relevant Calculations [ Sample Size (n) = 14 ]

X	11	6	10	10	8	10	17	8	1 (Min)	10	7	5	19 (Max)	15	Sum = 137
X2	121	36	100	100	64	100	289	64	1	100	49	25	361	225	Sum = 1635

Thus, from the above table calculations, we get,

(i) The Range of the sample data is given as,

The Mean of the sample data is given as,

(ii) The Standard Deviation of the sample data is given as,

(iii) The Variance of the sample data is given as,

  

  

(iv) Now, we have to find out what important feature of the data is not revealed through the different measures of​ variation ..... !!

(Ans) We know that the above Measures of Dispersion that we have calculated such as Range, Standard Deviation and Variance tell us something about the sample data.

The Range of the Sample data reveals the difference between the largest number of hurricanes and the smallest number of hurricanes in the data. And, on the other hand both the Standard Deviation and Variance of the Sample data tell us about the Scale of the Data as well as the dispersion that is the spread of the data. But, the above measures of dispersion do not reveal any information about the pattern of the data over time.

Thus, the important feature of the data that is not revealed through the different measures of​ variation is the Pattern of the Sample data over time.

Thus, the Correct Answers are,

_________________________________